Chapter 48: Problem 4

Question: Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the transmitted light is one-third the intensity of the incident beam? Assume that each polarizing shjeet is ideal, that is that it reduces the intensity of unpolarized light by exactly $50\%$.

Solution: From our lectures we know that the intensity of transmitted light for these two sheets at an angle $\theta$ is

$$I(\theta)~=~I_0 {1\over 2}\cos^2\theta$$

from which we require that

$$\cos^2\theta~=~{2\over 3}$$

and hence $\theta~=~35.2^o$.